# Towards a conjecture on the distance spectral radius of trees

###
Valisoa Razanajatovo Misanantenaina

Stellenbosch University

####
Stephan Wagner

Stellenbosch University

####
Kenneth Dadedzi

Stellenbosch University

PDF

**Minisymposium:**
SPECTRAL GRAPH THEORY

**Content:**
The distance matrix of a graph is the matrix whose entry in the $i$th row, $j$th column is the distance $d(v_i,v_j)$ between the $i$th vertex $v_i$ and the $j$th vertex $v_j$. A conjecture of Ili\'c and Stevanovi\'c states that among all trees with given order and maximum degree, the so-called Volkmann trees minimise the spectral radius of the distance matrix.
In this talk, we present our recent progress towards this conjecture and its analogue for a ``reversed'' version of the distance matrix. Our ideas are based on similar results for the Wiener index and the spectral radius of the adjacency matrix.